Chris Nash made 52 and Joe Gatting 45 not out as Sussex set a daunting total of 209 for six, the second highest in the competition this season.
Some big hitting from Mark Pettini (44) and James Foster (47) - who struck four successive sixes at one stage - kept Essex in contention but they fell short in the end.
Unbeaten Sussex move on to eight points with the win, two points clear of nearest challengers Essex and three clear of third-placed Kent, who slumped to a six-wicket defeat against Hampshire at Canterbury.
Kent were seeking back-to-back wins over Hampshire after beating the Royals by three runs on Friday night, and they thought they had a good chance when Darren Stevens' 60 off 44 balls took them to 135 for six from their 20 overs on a tricky, seaming pitch.
However, Hampshire gained revenge for their home defeat two nights ago thanks to Glenn Maxwell, who clubbed a spectacular 66 not out from just 32 balls.
The Australian, having come to the wicket with his side struggling on 59 for four in the 11th over, struck half-a-dozen sixes and five fours to help Hampshire claim their first win of the season with 10 balls remaining.
Meanwhile, joint North Group leaders Yorkshire and Nottinghamshire were forced to share the points when bad weather had the final say in their clash on a damp afternoon at Scarborough.
Although the match began promptly on the sodden North Marine Road ground, there were two stoppages to the Nottinghamshire innings before the game was finally called off with the visitors on 105 for three after 14 overs.